Amazingly, Poincaré symmetry, the first few leading soft theorems employed in [1]}, and their local enhancements do not exhaust the list of known symmetries of asymptotically flat spacetimes. In addition, the symmetries arising from the first few leading soft theorems are at the very least augmented by an infinite tower [2]}. These arise from further subleading soft theorems [3]}, [4]} and, with an appropriate labelling, generate a \({\rm w}_{1+ \infty }\)  Kac-Moody symmetry [5]}. More precisely, these operators form a current algebra for the global “wedge subalgebra"For example, \({\rm SL}(2, \mathbb {R})\)  is the wedge subalgebra of (one copy of) Virasoro. of \({\rm w}_{1+ \infty }\) .
